Relationship between a natural number and its digital product

Laurențiu Panaitopol
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 10, 2004, Number 3, Pages 68—71
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Authors and affiliations

Laurențiu Panaitopol
University of Bucharest, Faculty of Mathematics
14 Academiei St., RO–010014 Bucharest, Romania

Abstract

For the integer number n ≥ 1 written in the basis b ≥ 2, we denote by sb(n), pb(n) and db(n) the sum, the product and the number of its digits, respectively. There are a series of more recent or older papers concerning the relationship between these numbers. For instance, one proves in {2} that, if b ≥ 3, then for infinitely many numbers m there exists n with db(n) = m and sb(n) = m, and this property fails also for infinitely many values of m.

Keywords

  • Sums and products of digits
  • Inequalities
  • Means

AMS Classification

  • 11A25
  • 11A51

References

  1. R.E. Kennedy, C. Cooper, A generalization of a result by Narkiewicz concerning large digits of powers. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 11(2000), 36–40 (2001).
  2. L. Panaitopol, On the relation between the digital sum and product of a natural number (in press).

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Cite this paper

APA

Panaitopol, L. (2004). Relationship between a natural number and its digital product. Notes on Number Theory and Discrete Mathematics, 10(3), 68-71.

Chicago

Panaitopol, Laurențiu. “Relationship between a Natural Number and Its Digital Product.” Notes on Number Theory and Discrete Mathematics 10, no. 3 (2004): 68-71.

MLA

Panaitopol, Laurențiu. “Relationship between a Natural Number and Its Digital Product.” Notes on Number Theory and Discrete Mathematics 10.3 (2004): 68-71. Print.

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